Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches

For the analytical description of the relationship between undercoolings, lamellar spacings and growth velocities during the directional solidification of ternary eutectics in 2D and 3D, different extensions based on the theory of Jackson and Hunt are reported in the literature. Besides analytical approaches, the phase-field method has been established to study the spatially complex microstructure evolution during the solidification of eutectic alloys. The understanding of the fundamental mechanisms controlling the morphology development in multiphase, multicomponent systems is of high interest. For this purpose, a comparison is made between the analytical extensions and three-dimensional phase-field simulations of directional solidification in an ideal ternary eutectic system. Based on the observed accordance in two-dimensional validation cases, the experimentally reported, inherently three-dimensional chain-like pattern is investigated in extensive simulation studies. The results are quantitatively compared with the analytical results reported in the literature, and with a newly derived approach which uses equal undercoolings. A good accordance of the undercooling–spacing characteristics between simulations and the analytical Jackson–Hunt apporaches are found. The results show that the applied phase-field model, which is based on the Grand potential approach, is able to describe the analytically predicted relationship between the undercooling and the lamellar arrangements during the directional solidification of a ternary eutectic system in 3D.